Question17 Write an equation of the line below in slope intercept form: $y=m x+b$

Studdy Solution

STEP 1

What is this asking? We need to find the equation of a line in the form $y = mx + b$ , given a graph showing the line passing through $(0, 1)$ and $(4, -1)$ . Watch out! Don't mix up the x and y coordinates!
Also, remember that the b in the equation is the y-intercept, not the x-intercept!

STEP 2

1. Find the slope.
2. Find the y-intercept.
3. Write the equation.

STEP 3

Alright, let's start by finding the slope, which tells us how steep our line is!
The slope, usually represented by m, is the change in y divided by the change in x.
We can use our two given points to find this.

STEP 4

Our points are $(0, 1)$ and $(4, -1)$ .
Let's label them!
Let's call $(0, 1)$ point 1, so $x_1 = 0$ and $y_1 = 1$ .
And $(4, -1)$ is point 2, so $x_2 = 4$ and $y_2 = -1$ .

STEP 5

The formula for the slope is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Let's plug in those values! $m = \frac{-1 - 1}{4 - 0}$ $m = \frac{-2}{4}$ $m = -\frac{1}{2}$ So, our slope is $-\frac{1}{2}$ !
This means for every 1 unit we move to the right along the x-axis, we move down $\frac{1}{2}$ a unit along the y-axis.

STEP 6

The y-intercept is the point where the line crosses the y-axis.
This happens when $x = 0$ .
Look closely at the graph!
We're given the point $(0, 1)$ , which means our line crosses the y-axis at $y = 1$ .
So, our y-intercept, which we call b, is 1!

STEP 7

We've got our slope, $m = -\frac{1}{2}$ , and our y-intercept, $b = 1$ .
Now we just plug them into the slope-intercept form: $y = mx + b$ $y = -\frac{1}{2}x + 1$ And there we have it!

STEP 8

The equation of the line is $y = -\frac{1}{2}x + 1$ .

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